1. Field of the Invention
The present invention relates to an apparatus for stabilizing cut-off frequency using a transconductance, and more specifically, to an apparatus for stabilizing cut-off frequency using a transconductance, capable of maintaining constant frequency characteristics regardless of changes in the temperature, changes in the power supply voltage and errors in fabrication, when a filter circuit is installed in an IC (Integrated Circuit).
2. Description of the Related Art
A demand for fabricating a filter into an integrated circuit, which is a matter of primary concern in an electronics industry, has shown an extreme interest in an SCF (Switched-Capacitor Filter) since the late 1970s. At the present, the SCF is commonly used through a MOSIC (Metal Oxide Semiconductor Integrated Circuit) technology.
For fabrication reasons, an active filter constructed with active elements, typically determines its accurate characteristics by adjusting resistance at the last process, which is a serious obstacle to fabricate the active filter into a complete IC.
A suggestion for overcoming such an obstacle is the SCF consisting of a switching device, a capacitor, and an operational amplifier. The operation characteristics of the SCF can be determined by the capacitor ratio that is suitable for easy fabrication of the filter into the IC.
Resistance used in the active filter can be substituted with the switching device switched by a predetermined switching frequency and the capacitor. The switching device can be easily fabricated using a MOSFET (Metal Oxide Semiconductor Field Effect Transistor). Accordingly, the integration of the filter is realized.
FIG. 1A is a conceptive circuit diagram embodying a resistance using a known switch 1 and a known capacitor C.sub.R. FIG. 1B is an equivalent circuit diagram of FIG. 1A. The switch 1 is turned on/off according to a predetermined switching frequency.
FIG. 1C is a circuit diagram of a real embodiment of FIG. 1A. Clock signals in an inverted phase as compared to each other, are supplied to gate terminals of transistors Q.sub.1 and Q.sub.2, respectively. The transistors Q.sub.1 and Q.sub.2 are then exclusively turned on/off. A voltage V.sub.1 input into the circuit is charged and discharged. As a result, a filtered frequency voltage V.sub.2 is output.
When the transistor Q.sub.1 is turned on, the capacitor C.sub.R is charged to C.sub.R .times.V.sub.1. When the transistor Q.sub.2 is turned on at the same time that the transistor Q.sub.1 is turned off, the capacitor C.sub.R is discharged to C.sub.R .times.V.sub.2.
The value of the charge q transmitted from the input to the output, is EQU q=C.sub.R (V1-V2) (1)
The charge q is transmitted for a switching period T.sub.c, current i(t) is, on an average, ##EQU1##
When a resistance corresponding to T.sub.C /C.sub.R is connected between input and output terminals, Eq. 2 shows the relationship between flowing current and voltage drop. Accordingly, an equivalent resistance that is approximately calculated by the following Eq. 3 is supposed to be connected between the input and the output terminals. ##EQU2## where f.sub.c is the inverse of the switching period T.sub.C, i.e., switching frequency.
Based on the theory, the resistance that is an obstacle to integration can be substituted with the switching device and the capacitor.
FIG. 2A is a circuit diagram of an active filter embodied using a resistance. The active filter consists of: a resistance R.sub.C for controlling an input voltage V.sub.1 ; an operational amplifier 2 outputting an output voltage V.sub.out by amplifying a signal generated from the resistance R.sub.c ; and a capacitor C.sub.1 for feeding back the output from the operational amplifier 2. The output voltage V.sub.out is, ##EQU3## where w is angular velocity of an input signal, and f.sub.1 is a frequency of the input signal.
FIG. 2B is a circuit diagram of an SCF embodied using FIG. 1A, consisting of: a switch 1 for sampling an input voltage V.sub.1 as a predetermined frequency; a capacitor C.sub.R for charging and discharging the voltage input into the switch 1; an operational amplifier 3 outputting an output voltage V.sub.out by amplifying a signal generated from the switch 1; and a capacitor C.sub.2 for feeding back the voltage of a frequency to be filtered out of outputs from the operational amplifier 3. The capacitor C.sub.R for charging and discharging the voltage input into the switch 1, and the resistance R.sub.c has a relationship of Eq. 3. The output voltage V.sub.out is, ##EQU4## where w is an angular velocity of an input signal, and f.sub.1 and f.sub.c are the frequency of the input signal and a switching frequency, respectively.
When the filter circuits of FIGS. 2A and 2B are installed in an IC, the resistance and the capacitor cause an error of approximately .+-.20%, respectively, due to a fabrication error. Therefore, a wanted cut-off frequency for the filter circuit can be obtained by changing the switching frequency f.sub.c. The switching frequency should be at least more than two times the frequency of the input signal according to Sampling theory. For a sufficient approximation to the resistance, typically, a switching frequency of more than ten times the frequency of the input signal is required.
However, the filter circuit installed in a conventional IC is limited to a low frequency filter because it cannot include an unlimited increase in switching frequency f.sub.c. Additionally, noise is inevitably generated in the switching frequency f.sub.c, which causes an instability of the circuit.